Theorem simp3i 1141

Description: Infer a conjunct from a triple conjunction. (Contributed by NM, 19-Apr-2005.)

Hypothesis

Ref	Expression
3simp1i.1	⊢ (𝜑 ∧ 𝜓 ∧ 𝜒)

Assertion

Ref	Expression
simp3i	⊢ 𝜒

Proof of Theorem simp3i

Step	Hyp	Ref	Expression
1		3simp1i.1	. 2 ⊢ (𝜑 ∧ 𝜓 ∧ 𝜒)
2		simp3 1138	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜒)
3	1, 2	ax-mp 5	1 ⊢ 𝜒

Syntax hints:   ∧ w3a 1086

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 207  df-an 396  df-3an 1088

This theorem is referenced by:  hartogslem2  9424  harwdom  9472  divalglem6  16304  structfn  17062  strleun  17063  oppchomfval  17615  sratset  21112  srads  21114  tngip  24557  dfrelog  26496  log2ub  26881  birthdaylem3  26885  birthday  26886  divsqrtsum2  26915  harmonicbnd2  26937  lgslem4  27233  lgscllem  27237  lgsdir2lem2  27259  lgsdir2lem3  27260  mulog2sumlem1  27467  siilem2  30824  h2hva  30946  h2hsm  30947  h2hnm  30948  elunop2  31985  wallispilem3  46105  wallispilem4  46106  prstchomval  49591  cnelsubclem  49635